BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gergo Kiss (Budapest Corvinus University and R\\' enyi Institute) DTSTART:20250522T130000Z DTEND:20250522T132500Z DTSTAMP:20260423T010337Z UID:CANT2025/6 DESCRIPTION:Title: Weak tiling and the Coven-Meyerowitz conjecture\nby Gergo Kiss (Budap est Corvinus University and R\\' enyi Institute) as part of Combinatorial and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Ce nter - Science Center (4th floor).\n\nAbstract\nThe concept of weak tiling was originally introduced in $\\mathbb{R}^n$ by Lev and Matolcsi\, and ha s proven to be an essential tool in addressing Fuglede's conjecture for co nvex domains. In this talk\, we extend the notion of weak tiling to the se tting of cyclic groups and further generalize it using a natural averaging process. As a result\, the tiles are no longer sets\, \nbut rather become step functions--a framework we refer to as functional tiling.\n\nOne adva ntage of this approach is that the cyclotomic divisors of the functions in volved in a functional tiling remain the same as those of the characterist ic functions of the original sets. Another is that functional tilings can be studied using the well-established tools and objective functions of lin ear programming\, which is computationally efficient due to its polynomial -time solvability.\n\nI will introduce the key quantities involved and pre sent basic connections between functional and classical tilings. Finally\, I will provide a counterexample to the Coven-Meyerowitz conjecture within the context of functional tilings. It is important to note\, however\, th at none of the counterexamples we constructed in this setting correspond t o tiling pairs of sets. Thus\, the Coven-Meyerowitz conjecture for tiling sets remains open.\nThis is joint work with Itay Londner\, M\\' at\\' e Ma tolcsi\, and G\\' abor Somlai.\n LOCATION:https://researchseminars.org/talk/CANT2025/6/ END:VEVENT END:VCALENDAR